New in Blender (coming from Modo)
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If you have the 3DView Transform Panel (N) open, it will show you the coordinates of a vertex. You can use an arithmethic operation if you want to offset a value. E.g. if the vertex is at (1, 2, 3) and you want to move it 4.5 units along Y, then you can simply double click into the Y field of the vertex transform. It will now read 2m followed by the cursor. Typing +4.5 and pressing &#9166; Enter will shift it to 6.5 as expected.

You can also use the operation properties which appears in the box after completing an operation. Press GY and confirm with  LMB to move the vertex along Y. The operation dialog will show




Move X       0m
     Y       0.12345m
     Z       0m


Now you can change the the relative value, by clicking on the individual field, entering it and confirming with &#9166; Enter or  LMB.



The BoolTools Addon is not yet updated for 2.8. (25.12.19)
In Object Mode (&#8633; Tab if you're in edit mode): Press &#9096; CtrlNumber to change the view level of the subdivision surface modifier. &#9096; Ctrl1 will be level one while &#9096; Ctrl0 will show no subdivision at all, etc...

The gizmo is enabled with the buttons on the left hand side T or with Space > G/R/S/3
Questions 1 - 4 are almost right for this forum, view the asking section for more info. They should however be split into several posts in the future. This question  may get closed for that reason. Question 5 however, does not have anything to do with the usage of Blender, but with the  usage of this forum. It belongs to meta.